Quorum-sensing active particles with discontinuous motility

TL;DR

This paper develops a mean-field theory for active particles with discontinuous motility responses to chemical signals, explaining aggregation phenomena and collective behaviors, supported by analytical solutions and numerical simulations.

Contribution

It introduces a novel model of active particles with threshold-based motility changes and provides analytical solutions for density profiles, advancing understanding of active matter with discontinuous responses.

Findings

Analytical solutions for density and polarization profiles in simple geometries.

Agreement between theory and numerical simulations using an effective diffusion coefficient.

Chemical gradient response can induce vortex cluster formation.

Abstract

We develop a dynamic mean-field theory for polar active particles that interact through a self-generated field, in particular one generated through emitting a chemical signal. While being a form of chemotactic response, it is different from conventional chemotaxis in that particles discontinuously change their motility when the local concentration surpasses a threshold. The resulting coupled equations for density and polarization are linear and can be solved analytically for simple geometries, yielding inhomogeneous density profiles. Specifically, here we consider a planar and circular interface. Our theory thus explains the observed coexistence of dense aggregates with an active gas. There are, however, differences to the more conventional picture of liquid-gas coexistence based on a free energy, most notably the absence of a critical point. We corroborate our analytical predictions by numerical simulations of active particles under confinement and interacting through volume exclusion. Excellent quantitative agreement is reached through an effective translational diffusion coefficient. We finally show that an additional response to the chemical gradient direction is sufficient to induce vortex clusters. Our results pave the way to engineer motility responses in order to achieve aggregation and collective behavior even at unfavorable conditions.